.64 



9. The products of the alternate sides of the circumscribed 

 hexagon are equal, viz : A/ Bg Ch— kg BA C/. 



10. The properties in (&) and (9) hold good in the more 

 general case ; that is, when the angles A C A2 = B C Bg ; 

 C A C3 = B A B., ; A B A3 = C B Co ; and these angles may 

 be taken either internally or externally with respect to the 

 original triangle ABC. 



Many other relations might be deduced from the appro- 

 priate diagrams; but the preceding appear to be the most 

 important. 



A Paper was read by W. Fairbairn, LL.D., &c., " On 

 the Temperature of the Earth's Crust, as exhibited by Ther- 

 mometrical Observations obtained during the sinking of the 

 Deep Mine at Dukinfield." 



During the prosecution of researches on the conductivity 

 and fusion of various substances, an opportunity occurred of 

 ascertaining by direct experiments, under favourable circum- 

 stances, the increase of temperature in the crust of the earth. 

 This was obtained by means of thermometers placed in bore- 

 holes, at various depths, during the sinking of one of the 

 deepest mines in England, namely, the coal mine belonging 

 to F. D. Astley, Esq., at Dukinfield, which has been sunk to a 

 depth of 700 yards. 



The increase of temperature in descending, shown by these 

 observations, is irregular ; nor is this to be wondered at, if we 

 consider the difficulties of the enquiry and the sources of error 

 in assuming the temperature in a single bore-hole, as the mean 

 temperature of the stratum. At the same time it is not 

 probable that the temperature in the mine-shaft influenced the 

 results. The rate of increase has been shown in previous 

 experiments to be directly as the depth, and this is confirmed 

 by these experiments. The amount of increase is from 51° F. 

 to 57|°, as the depth increases from 5§ to 231 yards, or 1° in 

 99 feet ; but, in this case, the higher temperature is not very 



